C2-algebra isomorphism conjecture for the chiral differential operators on quiver varieties

Let $\widetilde\CM(Q,\mathbf v,\mathbf w|\mathbf d)$ be the universal Poisson deformation of the relevant quiver variety, and let $\mathsf D^{\mathrm{ch}}(\widetilde\CM)$ denote its chiral differential operator vertex algebra. The preceding construction gives a natural Poisson-algebra map

$$\CR(\mathsf D^{\mathrm{ch}}(\widetilde\CM))\longrightarrow \mathscr O_{\widetilde\CM(Q,\mathbf v,\mathbf w|\mathbf d)}(\widetilde\CM).$$

C2-algebra isomorphism conjecture. The map above is an isomorphism. This would identify the $C_2$ algebra of the chiral differential operator vertex algebra with the function algebra of the corresponding quiver variety.